# Properties

 Label 336.4.h.b.239.7 Level $336$ Weight $4$ Character 336.239 Analytic conductor $19.825$ Analytic rank $0$ Dimension $24$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 336.h (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$19.8246417619$$ Analytic rank: $$0$$ Dimension: $$24$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 239.7 Character $$\chi$$ $$=$$ 336.239 Dual form 336.4.h.b.239.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.33643 - 4.64124i) q^{3} -12.0055i q^{5} +7.00000i q^{7} +(-16.0822 + 21.6878i) q^{9} +O(q^{10})$$ $$q+(-2.33643 - 4.64124i) q^{3} -12.0055i q^{5} +7.00000i q^{7} +(-16.0822 + 21.6878i) q^{9} -33.9879 q^{11} -13.8712 q^{13} +(-55.7206 + 28.0501i) q^{15} -28.7374i q^{17} +75.7520i q^{19} +(32.4887 - 16.3550i) q^{21} -104.296 q^{23} -19.1331 q^{25} +(138.233 + 23.9692i) q^{27} -242.660i q^{29} +316.604i q^{31} +(79.4103 + 157.746i) q^{33} +84.0388 q^{35} +303.265 q^{37} +(32.4091 + 64.3795i) q^{39} +382.946i q^{41} +12.0228i q^{43} +(260.374 + 193.076i) q^{45} -314.619 q^{47} -49.0000 q^{49} +(-133.377 + 67.1430i) q^{51} +418.518i q^{53} +408.043i q^{55} +(351.583 - 176.989i) q^{57} -477.106 q^{59} +112.267 q^{61} +(-151.815 - 112.575i) q^{63} +166.531i q^{65} +180.543i q^{67} +(243.680 + 484.062i) q^{69} -25.4197 q^{71} -349.113 q^{73} +(44.7032 + 88.8015i) q^{75} -237.915i q^{77} +452.651i q^{79} +(-211.725 - 697.577i) q^{81} +1081.66 q^{83} -345.009 q^{85} +(-1126.24 + 566.957i) q^{87} -816.177i q^{89} -97.0984i q^{91} +(1469.44 - 739.724i) q^{93} +909.444 q^{95} -1070.07 q^{97} +(546.600 - 737.124i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24 q - 136 q^{9} + O(q^{10})$$ $$24 q - 136 q^{9} + 96 q^{13} - 112 q^{21} + 168 q^{25} - 320 q^{33} - 864 q^{37} + 592 q^{45} - 1176 q^{49} - 1120 q^{57} - 2304 q^{61} + 1168 q^{69} + 3312 q^{73} - 968 q^{81} - 5808 q^{85} + 1776 q^{93} + 6480 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$$.

 $$n$$ $$85$$ $$113$$ $$127$$ $$241$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −2.33643 4.64124i −0.449646 0.893207i
$$4$$ 0 0
$$5$$ 12.0055i 1.07381i −0.843643 0.536904i $$-0.819594\pi$$
0.843643 0.536904i $$-0.180406\pi$$
$$6$$ 0 0
$$7$$ 7.00000i 0.377964i
$$8$$ 0 0
$$9$$ −16.0822 + 21.6878i −0.595637 + 0.803254i
$$10$$ 0 0
$$11$$ −33.9879 −0.931612 −0.465806 0.884887i $$-0.654236\pi$$
−0.465806 + 0.884887i $$0.654236\pi$$
$$12$$ 0 0
$$13$$ −13.8712 −0.295937 −0.147968 0.988992i $$-0.547273\pi$$
−0.147968 + 0.988992i $$0.547273\pi$$
$$14$$ 0 0
$$15$$ −55.7206 + 28.0501i −0.959133 + 0.482834i
$$16$$ 0 0
$$17$$ 28.7374i 0.409991i −0.978763 0.204996i $$-0.934282\pi$$
0.978763 0.204996i $$-0.0657180\pi$$
$$18$$ 0 0
$$19$$ 75.7520i 0.914668i 0.889295 + 0.457334i $$0.151196\pi$$
−0.889295 + 0.457334i $$0.848804\pi$$
$$20$$ 0 0
$$21$$ 32.4887 16.3550i 0.337600 0.169950i
$$22$$ 0 0
$$23$$ −104.296 −0.945530 −0.472765 0.881189i $$-0.656744\pi$$
−0.472765 + 0.881189i $$0.656744\pi$$
$$24$$ 0 0
$$25$$ −19.1331 −0.153065
$$26$$ 0 0
$$27$$ 138.233 + 23.9692i 0.985297 + 0.170848i
$$28$$ 0 0
$$29$$ 242.660i 1.55382i −0.629612 0.776910i $$-0.716786\pi$$
0.629612 0.776910i $$-0.283214\pi$$
$$30$$ 0 0
$$31$$ 316.604i 1.83432i 0.398523 + 0.917158i $$0.369523\pi$$
−0.398523 + 0.917158i $$0.630477\pi$$
$$32$$ 0 0
$$33$$ 79.4103 + 157.746i 0.418896 + 0.832122i
$$34$$ 0 0
$$35$$ 84.0388 0.405862
$$36$$ 0 0
$$37$$ 303.265 1.34747 0.673737 0.738971i $$-0.264688\pi$$
0.673737 + 0.738971i $$0.264688\pi$$
$$38$$ 0 0
$$39$$ 32.4091 + 64.3795i 0.133067 + 0.264333i
$$40$$ 0 0
$$41$$ 382.946i 1.45869i 0.684148 + 0.729343i $$0.260174\pi$$
−0.684148 + 0.729343i $$0.739826\pi$$
$$42$$ 0 0
$$43$$ 12.0228i 0.0426385i 0.999773 + 0.0213193i $$0.00678664\pi$$
−0.999773 + 0.0213193i $$0.993213\pi$$
$$44$$ 0 0
$$45$$ 260.374 + 193.076i 0.862541 + 0.639600i
$$46$$ 0 0
$$47$$ −314.619 −0.976424 −0.488212 0.872725i $$-0.662351\pi$$
−0.488212 + 0.872725i $$0.662351\pi$$
$$48$$ 0 0
$$49$$ −49.0000 −0.142857
$$50$$ 0 0
$$51$$ −133.377 + 67.1430i −0.366207 + 0.184351i
$$52$$ 0 0
$$53$$ 418.518i 1.08468i 0.840160 + 0.542338i $$0.182461\pi$$
−0.840160 + 0.542338i $$0.817539\pi$$
$$54$$ 0 0
$$55$$ 408.043i 1.00037i
$$56$$ 0 0
$$57$$ 351.583 176.989i 0.816988 0.411277i
$$58$$ 0 0
$$59$$ −477.106 −1.05278 −0.526389 0.850244i $$-0.676454\pi$$
−0.526389 + 0.850244i $$0.676454\pi$$
$$60$$ 0 0
$$61$$ 112.267 0.235644 0.117822 0.993035i $$-0.462409\pi$$
0.117822 + 0.993035i $$0.462409\pi$$
$$62$$ 0 0
$$63$$ −151.815 112.575i −0.303601 0.225130i
$$64$$ 0 0
$$65$$ 166.531i 0.317779i
$$66$$ 0 0
$$67$$ 180.543i 0.329207i 0.986360 + 0.164604i $$0.0526345\pi$$
−0.986360 + 0.164604i $$0.947366\pi$$
$$68$$ 0 0
$$69$$ 243.680 + 484.062i 0.425154 + 0.844554i
$$70$$ 0 0
$$71$$ −25.4197 −0.0424896 −0.0212448 0.999774i $$-0.506763\pi$$
−0.0212448 + 0.999774i $$0.506763\pi$$
$$72$$ 0 0
$$73$$ −349.113 −0.559734 −0.279867 0.960039i $$-0.590290\pi$$
−0.279867 + 0.960039i $$0.590290\pi$$
$$74$$ 0 0
$$75$$ 44.7032 + 88.8015i 0.0688251 + 0.136719i
$$76$$ 0 0
$$77$$ 237.915i 0.352116i
$$78$$ 0 0
$$79$$ 452.651i 0.644648i 0.946629 + 0.322324i $$0.104464\pi$$
−0.946629 + 0.322324i $$0.895536\pi$$
$$80$$ 0 0
$$81$$ −211.725 697.577i −0.290433 0.956895i
$$82$$ 0 0
$$83$$ 1081.66 1.43046 0.715230 0.698889i $$-0.246322\pi$$
0.715230 + 0.698889i $$0.246322\pi$$
$$84$$ 0 0
$$85$$ −345.009 −0.440252
$$86$$ 0 0
$$87$$ −1126.24 + 566.957i −1.38788 + 0.698669i
$$88$$ 0 0
$$89$$ 816.177i 0.972075i −0.873938 0.486037i $$-0.838442\pi$$
0.873938 0.486037i $$-0.161558\pi$$
$$90$$ 0 0
$$91$$ 97.0984i 0.111854i
$$92$$ 0 0
$$93$$ 1469.44 739.724i 1.63842 0.824793i
$$94$$ 0 0
$$95$$ 909.444 0.982178
$$96$$ 0 0
$$97$$ −1070.07 −1.12009 −0.560046 0.828462i $$-0.689216\pi$$
−0.560046 + 0.828462i $$0.689216\pi$$
$$98$$ 0 0
$$99$$ 546.600 737.124i 0.554903 0.748321i
$$100$$ 0 0
$$101$$ 1356.15i 1.33606i 0.744134 + 0.668031i $$0.232863\pi$$
−0.744134 + 0.668031i $$0.767137\pi$$
$$102$$ 0 0
$$103$$ 757.734i 0.724872i 0.932009 + 0.362436i $$0.118055\pi$$
−0.932009 + 0.362436i $$0.881945\pi$$
$$104$$ 0 0
$$105$$ −196.351 390.044i −0.182494 0.362518i
$$106$$ 0 0
$$107$$ −987.341 −0.892055 −0.446027 0.895019i $$-0.647162\pi$$
−0.446027 + 0.895019i $$0.647162\pi$$
$$108$$ 0 0
$$109$$ −1257.53 −1.10504 −0.552522 0.833498i $$-0.686334\pi$$
−0.552522 + 0.833498i $$0.686334\pi$$
$$110$$ 0 0
$$111$$ −708.558 1407.53i −0.605886 1.20357i
$$112$$ 0 0
$$113$$ 449.026i 0.373812i −0.982378 0.186906i $$-0.940154\pi$$
0.982378 0.186906i $$-0.0598460\pi$$
$$114$$ 0 0
$$115$$ 1252.13i 1.01532i
$$116$$ 0 0
$$117$$ 223.079 300.836i 0.176271 0.237712i
$$118$$ 0 0
$$119$$ 201.162 0.154962
$$120$$ 0 0
$$121$$ −175.823 −0.132099
$$122$$ 0 0
$$123$$ 1777.35 894.727i 1.30291 0.655892i
$$124$$ 0 0
$$125$$ 1270.99i 0.909446i
$$126$$ 0 0
$$127$$ 1557.87i 1.08849i −0.838925 0.544247i $$-0.816816\pi$$
0.838925 0.544247i $$-0.183184\pi$$
$$128$$ 0 0
$$129$$ 55.8006 28.0904i 0.0380850 0.0191722i
$$130$$ 0 0
$$131$$ −1864.44 −1.24349 −0.621743 0.783221i $$-0.713575\pi$$
−0.621743 + 0.783221i $$0.713575\pi$$
$$132$$ 0 0
$$133$$ −530.264 −0.345712
$$134$$ 0 0
$$135$$ 287.764 1659.57i 0.183458 1.05802i
$$136$$ 0 0
$$137$$ 579.299i 0.361261i −0.983551 0.180631i $$-0.942186\pi$$
0.983551 0.180631i $$-0.0578139\pi$$
$$138$$ 0 0
$$139$$ 1410.44i 0.860661i −0.902671 0.430330i $$-0.858397\pi$$
0.902671 0.430330i $$-0.141603\pi$$
$$140$$ 0 0
$$141$$ 735.086 + 1460.22i 0.439045 + 0.872149i
$$142$$ 0 0
$$143$$ 471.453 0.275698
$$144$$ 0 0
$$145$$ −2913.26 −1.66851
$$146$$ 0 0
$$147$$ 114.485 + 227.421i 0.0642351 + 0.127601i
$$148$$ 0 0
$$149$$ 2848.23i 1.56601i 0.622013 + 0.783007i $$0.286315\pi$$
−0.622013 + 0.783007i $$0.713685\pi$$
$$150$$ 0 0
$$151$$ 556.913i 0.300138i −0.988675 0.150069i $$-0.952050\pi$$
0.988675 0.150069i $$-0.0479497\pi$$
$$152$$ 0 0
$$153$$ 623.253 + 462.161i 0.329327 + 0.244206i
$$154$$ 0 0
$$155$$ 3801.01 1.96971
$$156$$ 0 0
$$157$$ −1054.63 −0.536104 −0.268052 0.963405i $$-0.586380\pi$$
−0.268052 + 0.963405i $$0.586380\pi$$
$$158$$ 0 0
$$159$$ 1942.44 977.837i 0.968840 0.487720i
$$160$$ 0 0
$$161$$ 730.071i 0.357377i
$$162$$ 0 0
$$163$$ 2521.74i 1.21177i −0.795553 0.605884i $$-0.792820\pi$$
0.795553 0.605884i $$-0.207180\pi$$
$$164$$ 0 0
$$165$$ 1893.83 953.364i 0.893540 0.449814i
$$166$$ 0 0
$$167$$ 1267.63 0.587379 0.293689 0.955901i $$-0.405117\pi$$
0.293689 + 0.955901i $$0.405117\pi$$
$$168$$ 0 0
$$169$$ −2004.59 −0.912421
$$170$$ 0 0
$$171$$ −1642.90 1218.26i −0.734710 0.544810i
$$172$$ 0 0
$$173$$ 356.100i 0.156496i 0.996934 + 0.0782479i $$0.0249326\pi$$
−0.996934 + 0.0782479i $$0.975067\pi$$
$$174$$ 0 0
$$175$$ 133.932i 0.0578532i
$$176$$ 0 0
$$177$$ 1114.72 + 2214.36i 0.473377 + 0.940349i
$$178$$ 0 0
$$179$$ −4277.21 −1.78600 −0.893000 0.450057i $$-0.851404\pi$$
−0.893000 + 0.450057i $$0.851404\pi$$
$$180$$ 0 0
$$181$$ 3200.35 1.31426 0.657128 0.753779i $$-0.271771\pi$$
0.657128 + 0.753779i $$0.271771\pi$$
$$182$$ 0 0
$$183$$ −262.303 521.056i −0.105956 0.210479i
$$184$$ 0 0
$$185$$ 3640.87i 1.44693i
$$186$$ 0 0
$$187$$ 976.725i 0.381953i
$$188$$ 0 0
$$189$$ −167.785 + 967.634i −0.0645743 + 0.372407i
$$190$$ 0 0
$$191$$ 3437.92 1.30240 0.651201 0.758905i $$-0.274265\pi$$
0.651201 + 0.758905i $$0.274265\pi$$
$$192$$ 0 0
$$193$$ −4846.78 −1.80766 −0.903831 0.427889i $$-0.859258\pi$$
−0.903831 + 0.427889i $$0.859258\pi$$
$$194$$ 0 0
$$195$$ 772.912 389.088i 0.283843 0.142888i
$$196$$ 0 0
$$197$$ 1330.88i 0.481326i −0.970609 0.240663i $$-0.922635\pi$$
0.970609 0.240663i $$-0.0773648\pi$$
$$198$$ 0 0
$$199$$ 3197.38i 1.13898i 0.821999 + 0.569489i $$0.192859\pi$$
−0.821999 + 0.569489i $$0.807141\pi$$
$$200$$ 0 0
$$201$$ 837.945 421.827i 0.294050 0.148027i
$$202$$ 0 0
$$203$$ 1698.62 0.587289
$$204$$ 0 0
$$205$$ 4597.48 1.56635
$$206$$ 0 0
$$207$$ 1677.31 2261.95i 0.563193 0.759500i
$$208$$ 0 0
$$209$$ 2574.65i 0.852116i
$$210$$ 0 0
$$211$$ 85.7881i 0.0279900i 0.999902 + 0.0139950i $$0.00445490\pi$$
−0.999902 + 0.0139950i $$0.995545\pi$$
$$212$$ 0 0
$$213$$ 59.3912 + 117.979i 0.0191053 + 0.0379520i
$$214$$ 0 0
$$215$$ 144.340 0.0457856
$$216$$ 0 0
$$217$$ −2216.23 −0.693307
$$218$$ 0 0
$$219$$ 815.678 + 1620.32i 0.251682 + 0.499958i
$$220$$ 0 0
$$221$$ 398.623i 0.121332i
$$222$$ 0 0
$$223$$ 335.779i 0.100832i −0.998728 0.0504158i $$-0.983945\pi$$
0.998728 0.0504158i $$-0.0160546\pi$$
$$224$$ 0 0
$$225$$ 307.703 414.957i 0.0911713 0.122950i
$$226$$ 0 0
$$227$$ −3532.32 −1.03281 −0.516405 0.856344i $$-0.672730\pi$$
−0.516405 + 0.856344i $$0.672730\pi$$
$$228$$ 0 0
$$229$$ −5711.26 −1.64808 −0.824040 0.566531i $$-0.808285\pi$$
−0.824040 + 0.566531i $$0.808285\pi$$
$$230$$ 0 0
$$231$$ −1104.22 + 555.872i −0.314513 + 0.158328i
$$232$$ 0 0
$$233$$ 1026.46i 0.288607i 0.989534 + 0.144303i $$0.0460941\pi$$
−0.989534 + 0.144303i $$0.953906\pi$$
$$234$$ 0 0
$$235$$ 3777.18i 1.04849i
$$236$$ 0 0
$$237$$ 2100.86 1057.59i 0.575804 0.289863i
$$238$$ 0 0
$$239$$ −2404.61 −0.650800 −0.325400 0.945576i $$-0.605499\pi$$
−0.325400 + 0.945576i $$0.605499\pi$$
$$240$$ 0 0
$$241$$ −6537.60 −1.74740 −0.873700 0.486464i $$-0.838286\pi$$
−0.873700 + 0.486464i $$0.838286\pi$$
$$242$$ 0 0
$$243$$ −2742.94 + 2612.51i −0.724114 + 0.689681i
$$244$$ 0 0
$$245$$ 588.272i 0.153401i
$$246$$ 0 0
$$247$$ 1050.77i 0.270684i
$$248$$ 0 0
$$249$$ −2527.23 5020.27i −0.643200 1.27770i
$$250$$ 0 0
$$251$$ 76.2619 0.0191777 0.00958886 0.999954i $$-0.496948\pi$$
0.00958886 + 0.999954i $$0.496948\pi$$
$$252$$ 0 0
$$253$$ 3544.80 0.880867
$$254$$ 0 0
$$255$$ 806.088 + 1601.27i 0.197958 + 0.393236i
$$256$$ 0 0
$$257$$ 5213.42i 1.26539i 0.774403 + 0.632693i $$0.218051\pi$$
−0.774403 + 0.632693i $$0.781949\pi$$
$$258$$ 0 0
$$259$$ 2122.86i 0.509297i
$$260$$ 0 0
$$261$$ 5262.77 + 3902.50i 1.24811 + 0.925513i
$$262$$ 0 0
$$263$$ −6662.59 −1.56210 −0.781051 0.624468i $$-0.785316\pi$$
−0.781051 + 0.624468i $$0.785316\pi$$
$$264$$ 0 0
$$265$$ 5024.54 1.16473
$$266$$ 0 0
$$267$$ −3788.07 + 1906.94i −0.868264 + 0.437089i
$$268$$ 0 0
$$269$$ 5591.40i 1.26734i −0.773605 0.633669i $$-0.781548\pi$$
0.773605 0.633669i $$-0.218452\pi$$
$$270$$ 0 0
$$271$$ 2023.00i 0.453462i 0.973957 + 0.226731i $$0.0728039\pi$$
−0.973957 + 0.226731i $$0.927196\pi$$
$$272$$ 0 0
$$273$$ −450.657 + 226.863i −0.0999084 + 0.0502945i
$$274$$ 0 0
$$275$$ 650.295 0.142597
$$276$$ 0 0
$$277$$ 6383.29 1.38460 0.692300 0.721609i $$-0.256597\pi$$
0.692300 + 0.721609i $$0.256597\pi$$
$$278$$ 0 0
$$279$$ −6866.47 5091.70i −1.47342 1.09259i
$$280$$ 0 0
$$281$$ 7466.36i 1.58507i 0.609824 + 0.792537i $$0.291240\pi$$
−0.609824 + 0.792537i $$0.708760\pi$$
$$282$$ 0 0
$$283$$ 1593.17i 0.334644i −0.985902 0.167322i $$-0.946488\pi$$
0.985902 0.167322i $$-0.0535120\pi$$
$$284$$ 0 0
$$285$$ −2124.85 4220.95i −0.441633 0.877289i
$$286$$ 0 0
$$287$$ −2680.62 −0.551332
$$288$$ 0 0
$$289$$ 4087.16 0.831907
$$290$$ 0 0
$$291$$ 2500.14 + 4966.44i 0.503645 + 1.00047i
$$292$$ 0 0
$$293$$ 7812.67i 1.55775i 0.627179 + 0.778875i $$0.284210\pi$$
−0.627179 + 0.778875i $$0.715790\pi$$
$$294$$ 0 0
$$295$$ 5727.92i 1.13048i
$$296$$ 0 0
$$297$$ −4698.26 814.664i −0.917915 0.159164i
$$298$$ 0 0
$$299$$ 1446.71 0.279817
$$300$$ 0 0
$$301$$ −84.1594 −0.0161158
$$302$$ 0 0
$$303$$ 6294.23 3168.55i 1.19338 0.600754i
$$304$$ 0 0
$$305$$ 1347.82i 0.253036i
$$306$$ 0 0
$$307$$ 5120.06i 0.951848i 0.879486 + 0.475924i $$0.157886\pi$$
−0.879486 + 0.475924i $$0.842114\pi$$
$$308$$ 0 0
$$309$$ 3516.83 1770.39i 0.647460 0.325936i
$$310$$ 0 0
$$311$$ 7740.01 1.41124 0.705620 0.708590i $$-0.250668\pi$$
0.705620 + 0.708590i $$0.250668\pi$$
$$312$$ 0 0
$$313$$ 4208.89 0.760066 0.380033 0.924973i $$-0.375913\pi$$
0.380033 + 0.924973i $$0.375913\pi$$
$$314$$ 0 0
$$315$$ −1351.53 + 1822.62i −0.241746 + 0.326010i
$$316$$ 0 0
$$317$$ 8363.38i 1.48181i 0.671609 + 0.740905i $$0.265603\pi$$
−0.671609 + 0.740905i $$0.734397\pi$$
$$318$$ 0 0
$$319$$ 8247.49i 1.44756i
$$320$$ 0 0
$$321$$ 2306.85 + 4582.48i 0.401109 + 0.796789i
$$322$$ 0 0
$$323$$ 2176.92 0.375006
$$324$$ 0 0
$$325$$ 265.400 0.0452976
$$326$$ 0 0
$$327$$ 2938.14 + 5836.51i 0.496879 + 0.987033i
$$328$$ 0 0
$$329$$ 2202.34i 0.369054i
$$330$$ 0 0
$$331$$ 11782.9i 1.95663i −0.207111 0.978317i $$-0.566406\pi$$
0.207111 0.978317i $$-0.433594\pi$$
$$332$$ 0 0
$$333$$ −4877.18 + 6577.17i −0.802605 + 1.08236i
$$334$$ 0 0
$$335$$ 2167.52 0.353505
$$336$$ 0 0
$$337$$ 4424.50 0.715187 0.357593 0.933877i $$-0.383597\pi$$
0.357593 + 0.933877i $$0.383597\pi$$
$$338$$ 0 0
$$339$$ −2084.04 + 1049.12i −0.333892 + 0.168083i
$$340$$ 0 0
$$341$$ 10760.7i 1.70887i
$$342$$ 0 0
$$343$$ 343.000i 0.0539949i
$$344$$ 0 0
$$345$$ 5811.43 2925.51i 0.906889 0.456534i
$$346$$ 0 0
$$347$$ 3752.27 0.580497 0.290248 0.956951i $$-0.406262\pi$$
0.290248 + 0.956951i $$0.406262\pi$$
$$348$$ 0 0
$$349$$ 3908.60 0.599492 0.299746 0.954019i $$-0.403098\pi$$
0.299746 + 0.954019i $$0.403098\pi$$
$$350$$ 0 0
$$351$$ −1917.46 332.482i −0.291586 0.0505601i
$$352$$ 0 0
$$353$$ 2100.72i 0.316742i −0.987380 0.158371i $$-0.949376\pi$$
0.987380 0.158371i $$-0.0506242\pi$$
$$354$$ 0 0
$$355$$ 305.177i 0.0456257i
$$356$$ 0 0
$$357$$ −470.001 933.642i −0.0696781 0.138413i
$$358$$ 0 0
$$359$$ −3016.76 −0.443505 −0.221752 0.975103i $$-0.571178\pi$$
−0.221752 + 0.975103i $$0.571178\pi$$
$$360$$ 0 0
$$361$$ 1120.64 0.163382
$$362$$ 0 0
$$363$$ 410.799 + 816.038i 0.0593976 + 0.117991i
$$364$$ 0 0
$$365$$ 4191.29i 0.601047i
$$366$$ 0 0
$$367$$ 6833.27i 0.971918i 0.873982 + 0.485959i $$0.161530\pi$$
−0.873982 + 0.485959i $$0.838470\pi$$
$$368$$ 0 0
$$369$$ −8305.28 6158.62i −1.17170 0.868848i
$$370$$ 0 0
$$371$$ −2929.62 −0.409969
$$372$$ 0 0
$$373$$ 11866.5 1.64725 0.823627 0.567132i $$-0.191947\pi$$
0.823627 + 0.567132i $$0.191947\pi$$
$$374$$ 0 0
$$375$$ −5898.97 + 2969.58i −0.812323 + 0.408929i
$$376$$ 0 0
$$377$$ 3365.98i 0.459832i
$$378$$ 0 0
$$379$$ 13985.9i 1.89554i −0.318956 0.947769i $$-0.603332\pi$$
0.318956 0.947769i $$-0.396668\pi$$
$$380$$ 0 0
$$381$$ −7230.45 + 3639.85i −0.972250 + 0.489436i
$$382$$ 0 0
$$383$$ −7569.70 −1.00990 −0.504952 0.863147i $$-0.668490\pi$$
−0.504952 + 0.863147i $$0.668490\pi$$
$$384$$ 0 0
$$385$$ −2856.30 −0.378106
$$386$$ 0 0
$$387$$ −260.748 193.353i −0.0342495 0.0253971i
$$388$$ 0 0
$$389$$ 2949.39i 0.384422i 0.981354 + 0.192211i $$0.0615657\pi$$
−0.981354 + 0.192211i $$0.938434\pi$$
$$390$$ 0 0
$$391$$ 2997.20i 0.387659i
$$392$$ 0 0
$$393$$ 4356.13 + 8653.31i 0.559129 + 1.11069i
$$394$$ 0 0
$$395$$ 5434.32 0.692229
$$396$$ 0 0
$$397$$ −9934.24 −1.25588 −0.627941 0.778261i $$-0.716102\pi$$
−0.627941 + 0.778261i $$0.716102\pi$$
$$398$$ 0 0
$$399$$ 1238.92 + 2461.08i 0.155448 + 0.308792i
$$400$$ 0 0
$$401$$ 12531.7i 1.56060i −0.625403 0.780302i $$-0.715066\pi$$
0.625403 0.780302i $$-0.284934\pi$$
$$402$$ 0 0
$$403$$ 4391.68i 0.542842i
$$404$$ 0 0
$$405$$ −8374.79 + 2541.88i −1.02752 + 0.311869i
$$406$$ 0 0
$$407$$ −10307.4 −1.25532
$$408$$ 0 0
$$409$$ −9543.29 −1.15375 −0.576877 0.816831i $$-0.695729\pi$$
−0.576877 + 0.816831i $$0.695729\pi$$
$$410$$ 0 0
$$411$$ −2688.66 + 1353.49i −0.322681 + 0.162440i
$$412$$ 0 0
$$413$$ 3339.74i 0.397913i
$$414$$ 0 0
$$415$$ 12986.0i 1.53604i
$$416$$ 0 0
$$417$$ −6546.18 + 3295.39i −0.768748 + 0.386993i
$$418$$ 0 0
$$419$$ −889.368 −0.103696 −0.0518478 0.998655i $$-0.516511\pi$$
−0.0518478 + 0.998655i $$0.516511\pi$$
$$420$$ 0 0
$$421$$ 293.443 0.0339704 0.0169852 0.999856i $$-0.494593\pi$$
0.0169852 + 0.999856i $$0.494593\pi$$
$$422$$ 0 0
$$423$$ 5059.77 6823.42i 0.581595 0.784316i
$$424$$ 0 0
$$425$$ 549.838i 0.0627554i
$$426$$ 0 0
$$427$$ 785.866i 0.0890650i
$$428$$ 0 0
$$429$$ −1101.52 2188.12i −0.123967 0.246256i
$$430$$ 0 0
$$431$$ −7891.67 −0.881968 −0.440984 0.897515i $$-0.645370\pi$$
−0.440984 + 0.897515i $$0.645370\pi$$
$$432$$ 0 0
$$433$$ 10888.9 1.20851 0.604255 0.796791i $$-0.293471\pi$$
0.604255 + 0.796791i $$0.293471\pi$$
$$434$$ 0 0
$$435$$ 6806.63 + 13521.1i 0.750236 + 1.49032i
$$436$$ 0 0
$$437$$ 7900.61i 0.864846i
$$438$$ 0 0
$$439$$ 7101.91i 0.772109i −0.922476 0.386054i $$-0.873838\pi$$
0.922476 0.386054i $$-0.126162\pi$$
$$440$$ 0 0
$$441$$ 788.028 1062.70i 0.0850910 0.114751i
$$442$$ 0 0
$$443$$ 10843.3 1.16294 0.581468 0.813569i $$-0.302478\pi$$
0.581468 + 0.813569i $$0.302478\pi$$
$$444$$ 0 0
$$445$$ −9798.66 −1.04382
$$446$$ 0 0
$$447$$ 13219.3 6654.68i 1.39877 0.704151i
$$448$$ 0 0
$$449$$ 11771.1i 1.23722i −0.785698 0.618611i $$-0.787696\pi$$
0.785698 0.618611i $$-0.212304\pi$$
$$450$$ 0 0
$$451$$ 13015.5i 1.35893i
$$452$$ 0 0
$$453$$ −2584.76 + 1301.19i −0.268086 + 0.134956i
$$454$$ 0 0
$$455$$ −1165.72 −0.120109
$$456$$ 0 0
$$457$$ 15242.9 1.56025 0.780125 0.625624i $$-0.215155\pi$$
0.780125 + 0.625624i $$0.215155\pi$$
$$458$$ 0 0
$$459$$ 688.815 3972.48i 0.0700460 0.403964i
$$460$$ 0 0
$$461$$ 537.066i 0.0542595i 0.999632 + 0.0271298i $$0.00863673\pi$$
−0.999632 + 0.0271298i $$0.991363\pi$$
$$462$$ 0 0
$$463$$ 1043.87i 0.104780i −0.998627 0.0523898i $$-0.983316\pi$$
0.998627 0.0523898i $$-0.0166838\pi$$
$$464$$ 0 0
$$465$$ −8880.78 17641.4i −0.885670 1.75935i
$$466$$ 0 0
$$467$$ 1482.78 0.146927 0.0734633 0.997298i $$-0.476595\pi$$
0.0734633 + 0.997298i $$0.476595\pi$$
$$468$$ 0 0
$$469$$ −1263.80 −0.124429
$$470$$ 0 0
$$471$$ 2464.06 + 4894.77i 0.241057 + 0.478851i
$$472$$ 0 0
$$473$$ 408.629i 0.0397226i
$$474$$ 0 0
$$475$$ 1449.37i 0.140004i
$$476$$ 0 0
$$477$$ −9076.75 6730.69i −0.871270 0.646074i
$$478$$ 0 0
$$479$$ −722.425 −0.0689111 −0.0344556 0.999406i $$-0.510970\pi$$
−0.0344556 + 0.999406i $$0.510970\pi$$
$$480$$ 0 0
$$481$$ −4206.65 −0.398767
$$482$$ 0 0
$$483$$ −3388.43 + 1705.76i −0.319211 + 0.160693i
$$484$$ 0 0
$$485$$ 12846.7i 1.20276i
$$486$$ 0 0
$$487$$ 3750.20i 0.348948i 0.984662 + 0.174474i $$0.0558226\pi$$
−0.984662 + 0.174474i $$0.944177\pi$$
$$488$$ 0 0
$$489$$ −11704.0 + 5891.87i −1.08236 + 0.544866i
$$490$$ 0 0
$$491$$ 5139.62 0.472399 0.236199 0.971705i $$-0.424098\pi$$
0.236199 + 0.971705i $$0.424098\pi$$
$$492$$ 0 0
$$493$$ −6973.42 −0.637053
$$494$$ 0 0
$$495$$ −8849.58 6562.23i −0.803553 0.595860i
$$496$$ 0 0
$$497$$ 177.938i 0.0160595i
$$498$$ 0 0
$$499$$ 13413.4i 1.20334i −0.798746 0.601668i $$-0.794503\pi$$
0.798746 0.601668i $$-0.205497\pi$$
$$500$$ 0 0
$$501$$ −2961.73 5883.38i −0.264113 0.524651i
$$502$$ 0 0
$$503$$ 9602.30 0.851184 0.425592 0.904915i $$-0.360066\pi$$
0.425592 + 0.904915i $$0.360066\pi$$
$$504$$ 0 0
$$505$$ 16281.3 1.43467
$$506$$ 0 0
$$507$$ 4683.58 + 9303.78i 0.410267 + 0.814981i
$$508$$ 0 0
$$509$$ 20047.2i 1.74573i −0.487962 0.872865i $$-0.662260\pi$$
0.487962 0.872865i $$-0.337740\pi$$
$$510$$ 0 0
$$511$$ 2443.79i 0.211560i
$$512$$ 0 0
$$513$$ −1815.72 + 10471.5i −0.156269 + 0.901220i
$$514$$ 0 0
$$515$$ 9097.02 0.778374
$$516$$ 0 0
$$517$$ 10693.2 0.909649
$$518$$ 0 0
$$519$$ 1652.75 832.002i 0.139783 0.0703677i
$$520$$ 0 0
$$521$$ 14178.2i 1.19224i 0.802894 + 0.596121i $$0.203292\pi$$
−0.802894 + 0.596121i $$0.796708\pi$$
$$522$$ 0 0
$$523$$ 3326.40i 0.278114i −0.990284 0.139057i $$-0.955593\pi$$
0.990284 0.139057i $$-0.0444071\pi$$
$$524$$ 0 0
$$525$$ −621.610 + 312.922i −0.0516749 + 0.0260134i
$$526$$ 0 0
$$527$$ 9098.40 0.752054
$$528$$ 0 0
$$529$$ −1289.38 −0.105974
$$530$$ 0 0
$$531$$ 7672.92 10347.4i 0.627074 0.845648i
$$532$$ 0 0
$$533$$ 5311.92i 0.431679i
$$534$$ 0 0
$$535$$ 11853.6i 0.957896i
$$536$$ 0 0
$$537$$ 9993.40 + 19851.6i 0.803067 + 1.59527i
$$538$$ 0 0
$$539$$ 1665.41 0.133087
$$540$$ 0 0
$$541$$ 1153.72 0.0916867 0.0458434 0.998949i $$-0.485402\pi$$
0.0458434 + 0.998949i $$0.485402\pi$$
$$542$$ 0 0
$$543$$ −7477.40 14853.6i −0.590950 1.17390i
$$544$$ 0 0
$$545$$ 15097.4i 1.18661i
$$546$$ 0 0
$$547$$ 25250.9i 1.97377i −0.161436 0.986883i $$-0.551613\pi$$
0.161436 0.986883i $$-0.448387\pi$$
$$548$$ 0 0
$$549$$ −1805.49 + 2434.82i −0.140358 + 0.189282i
$$550$$ 0 0
$$551$$ 18381.9 1.42123
$$552$$ 0 0
$$553$$ −3168.56 −0.243654
$$554$$ 0 0
$$555$$ −16898.1 + 8506.62i −1.29241 + 0.650606i
$$556$$ 0 0
$$557$$ 6469.49i 0.492138i −0.969252 0.246069i $$-0.920861\pi$$
0.969252 0.246069i $$-0.0791391\pi$$
$$558$$ 0 0
$$559$$ 166.770i 0.0126183i
$$560$$ 0 0
$$561$$ 4533.22 2282.05i 0.341163 0.171744i
$$562$$ 0 0
$$563$$ −19640.7 −1.47026 −0.735132 0.677924i $$-0.762880\pi$$
−0.735132 + 0.677924i $$0.762880\pi$$
$$564$$ 0 0
$$565$$ −5390.80 −0.401403
$$566$$ 0 0
$$567$$ 4883.04 1482.08i 0.361672 0.109773i
$$568$$ 0 0
$$569$$ 8396.74i 0.618646i 0.950957 + 0.309323i $$0.100102\pi$$
−0.950957 + 0.309323i $$0.899898\pi$$
$$570$$ 0 0
$$571$$ 4362.50i 0.319728i 0.987139 + 0.159864i $$0.0511056\pi$$
−0.987139 + 0.159864i $$0.948894\pi$$
$$572$$ 0 0
$$573$$ −8032.45 15956.2i −0.585620 1.16332i
$$574$$ 0 0
$$575$$ 1995.51 0.144728
$$576$$ 0 0
$$577$$ 19329.8 1.39465 0.697324 0.716756i $$-0.254374\pi$$
0.697324 + 0.716756i $$0.254374\pi$$
$$578$$ 0 0
$$579$$ 11324.2 + 22495.1i 0.812808 + 1.61462i
$$580$$ 0 0
$$581$$ 7571.65i 0.540663i
$$582$$ 0 0
$$583$$ 14224.5i 1.01050i
$$584$$ 0 0
$$585$$ −3611.71 2678.19i −0.255257 0.189281i
$$586$$ 0 0
$$587$$ −21737.9 −1.52848 −0.764241 0.644931i $$-0.776886\pi$$
−0.764241 + 0.644931i $$0.776886\pi$$
$$588$$ 0 0
$$589$$ −23983.4 −1.67779
$$590$$ 0 0
$$591$$ −6176.93 + 3109.50i −0.429924 + 0.216426i
$$592$$ 0 0
$$593$$ 20354.5i 1.40954i 0.709435 + 0.704771i $$0.248950\pi$$
−0.709435 + 0.704771i $$0.751050\pi$$
$$594$$ 0 0
$$595$$ 2415.06i 0.166400i
$$596$$ 0 0
$$597$$ 14839.8 7470.46i 1.01734 0.512137i
$$598$$ 0 0
$$599$$ 24269.5 1.65547 0.827733 0.561122i $$-0.189630\pi$$
0.827733 + 0.561122i $$0.189630\pi$$
$$600$$ 0 0
$$601$$ 20775.4 1.41006 0.705029 0.709178i $$-0.250934\pi$$
0.705029 + 0.709178i $$0.250934\pi$$
$$602$$ 0 0
$$603$$ −3915.60 2903.53i −0.264437 0.196088i
$$604$$ 0 0
$$605$$ 2110.85i 0.141849i
$$606$$ 0 0
$$607$$ 3498.28i 0.233922i 0.993136 + 0.116961i $$0.0373153\pi$$
−0.993136 + 0.116961i $$0.962685\pi$$
$$608$$ 0 0
$$609$$ −3968.70 7883.69i −0.264072 0.524570i
$$610$$ 0 0
$$611$$ 4364.15 0.288960
$$612$$ 0 0
$$613$$ 14449.4 0.952047 0.476024 0.879433i $$-0.342078\pi$$
0.476024 + 0.879433i $$0.342078\pi$$
$$614$$ 0 0
$$615$$ −10741.7 21338.0i −0.704303 1.39908i
$$616$$ 0 0
$$617$$ 14078.2i 0.918585i 0.888285 + 0.459293i $$0.151897\pi$$
−0.888285 + 0.459293i $$0.848103\pi$$
$$618$$ 0 0
$$619$$ 7166.47i 0.465339i 0.972556 + 0.232670i $$0.0747461\pi$$
−0.972556 + 0.232670i $$0.925254\pi$$
$$620$$ 0 0
$$621$$ −14417.2 2499.89i −0.931628 0.161541i
$$622$$ 0 0
$$623$$ 5713.24 0.367410
$$624$$ 0 0
$$625$$ −17650.6 −1.12964
$$626$$ 0 0
$$627$$ −11949.6 + 6015.48i −0.761116 + 0.383150i
$$628$$ 0 0
$$629$$ 8715.07i 0.552453i
$$630$$ 0 0
$$631$$ 8130.21i 0.512929i 0.966554 + 0.256465i $$0.0825577\pi$$
−0.966554 + 0.256465i $$0.917442\pi$$
$$632$$ 0 0
$$633$$ 398.163 200.438i 0.0250009 0.0125856i
$$634$$ 0 0
$$635$$ −18703.1 −1.16883
$$636$$ 0 0
$$637$$ 679.689 0.0422767
$$638$$ 0 0
$$639$$ 408.804 551.298i 0.0253084 0.0341299i
$$640$$ 0 0
$$641$$ 21601.6i 1.33106i −0.746370 0.665531i $$-0.768205\pi$$
0.746370 0.665531i $$-0.231795\pi$$
$$642$$ 0 0
$$643$$ 21818.4i 1.33816i 0.743192 + 0.669078i $$0.233311\pi$$
−0.743192 + 0.669078i $$0.766689\pi$$
$$644$$ 0 0
$$645$$ −337.240 669.916i −0.0205873 0.0408960i
$$646$$ 0 0
$$647$$ −26057.5 −1.58335 −0.791673 0.610945i $$-0.790790\pi$$
−0.791673 + 0.610945i $$0.790790\pi$$
$$648$$ 0 0
$$649$$ 16215.8 0.980781
$$650$$ 0 0
$$651$$ 5178.06 + 10286.1i 0.311742 + 0.619266i
$$652$$ 0 0
$$653$$ 8250.21i 0.494419i 0.968962 + 0.247209i $$0.0795136\pi$$
−0.968962 + 0.247209i $$0.920486\pi$$
$$654$$ 0 0
$$655$$ 22383.6i 1.33527i
$$656$$ 0 0
$$657$$ 5614.51 7571.51i 0.333398 0.449608i
$$658$$ 0 0
$$659$$ −7630.25 −0.451035 −0.225518 0.974239i $$-0.572407\pi$$
−0.225518 + 0.974239i $$0.572407\pi$$
$$660$$ 0 0
$$661$$ 1683.25 0.0990480 0.0495240 0.998773i $$-0.484230\pi$$
0.0495240 + 0.998773i $$0.484230\pi$$
$$662$$ 0 0
$$663$$ 1850.10 931.354i 0.108374 0.0545562i
$$664$$ 0 0
$$665$$ 6366.11i 0.371229i
$$666$$ 0 0
$$667$$ 25308.4i 1.46918i
$$668$$ 0 0
$$669$$ −1558.43 + 784.524i −0.0900634 + 0.0453385i
$$670$$ 0 0
$$671$$ −3815.71 −0.219529
$$672$$ 0 0
$$673$$ −16361.7 −0.937143 −0.468571 0.883426i $$-0.655231\pi$$
−0.468571 + 0.883426i $$0.655231\pi$$
$$674$$ 0 0
$$675$$ −2644.84 458.607i −0.150815 0.0261508i
$$676$$ 0 0
$$677$$ 13383.2i 0.759763i −0.925035 0.379882i $$-0.875965\pi$$
0.925035 0.379882i $$-0.124035\pi$$
$$678$$ 0 0
$$679$$ 7490.47i 0.423355i
$$680$$ 0 0
$$681$$ 8253.00 + 16394.3i 0.464399 + 0.922514i
$$682$$ 0 0
$$683$$ 15026.1 0.841810 0.420905 0.907105i $$-0.361713\pi$$
0.420905 + 0.907105i $$0.361713\pi$$
$$684$$ 0 0
$$685$$ −6954.80 −0.387926
$$686$$ 0 0
$$687$$ 13343.9 + 26507.3i 0.741053 + 1.47208i
$$688$$ 0 0
$$689$$ 5805.34i 0.320996i
$$690$$ 0 0
$$691$$ 1932.62i 0.106397i 0.998584 + 0.0531986i $$0.0169416\pi$$
−0.998584 + 0.0531986i $$0.983058\pi$$
$$692$$ 0 0
$$693$$ 5159.87 + 3826.20i 0.282839 + 0.209734i
$$694$$ 0 0
$$695$$ −16933.1 −0.924185
$$696$$ 0 0
$$697$$ 11004.9 0.598049
$$698$$ 0 0
$$699$$ 4764.03 2398.24i 0.257785 0.129771i
$$700$$ 0 0
$$701$$ 3730.63i 0.201004i 0.994937 + 0.100502i $$0.0320449\pi$$
−0.994937 + 0.100502i $$0.967955\pi$$
$$702$$ 0 0
$$703$$ 22972.9i 1.23249i
$$704$$ 0 0
$$705$$ 17530.8 8825.10i 0.936521 0.471451i
$$706$$ 0 0
$$707$$ −9493.07 −0.504984
$$708$$ 0 0
$$709$$ −19110.7 −1.01230 −0.506149 0.862446i $$-0.668931\pi$$
−0.506149 + 0.862446i $$0.668931\pi$$
$$710$$ 0 0
$$711$$ −9817.02 7279.62i −0.517816 0.383976i
$$712$$ 0 0
$$713$$ 33020.5i 1.73440i
$$714$$ 0 0
$$715$$ 5660.05i 0.296047i
$$716$$ 0 0
$$717$$ 5618.20 + 11160.4i 0.292630 + 0.581299i
$$718$$ 0 0
$$719$$ −9718.45 −0.504085 −0.252043 0.967716i $$-0.581102\pi$$
−0.252043 + 0.967716i $$0.581102\pi$$
$$720$$ 0 0
$$721$$ −5304.14 −0.273976
$$722$$ 0 0
$$723$$ 15274.6 + 30342.5i 0.785712 + 1.56079i
$$724$$ 0 0
$$725$$ 4642.84i 0.237836i
$$726$$ 0 0
$$727$$ 20385.8i 1.03998i 0.854172 + 0.519991i $$0.174065\pi$$
−0.854172 + 0.519991i $$0.825935\pi$$
$$728$$ 0 0
$$729$$ 18534.0 + 6626.70i 0.941622 + 0.336671i
$$730$$ 0 0
$$731$$ 345.504 0.0174814
$$732$$ 0 0
$$733$$ −14957.5 −0.753709 −0.376855 0.926272i $$-0.622994\pi$$
−0.376855 + 0.926272i $$0.622994\pi$$
$$734$$ 0 0
$$735$$ 2730.31 1374.45i 0.137019 0.0689762i
$$736$$ 0 0
$$737$$ 6136.29i 0.306693i
$$738$$ 0 0
$$739$$ 31710.5i 1.57847i −0.614090 0.789236i $$-0.710477\pi$$
0.614090 0.789236i $$-0.289523\pi$$
$$740$$ 0 0
$$741$$ −4876.88 + 2455.05i −0.241777 + 0.121712i
$$742$$ 0 0
$$743$$ 26608.9 1.31384 0.656922 0.753958i $$-0.271858\pi$$
0.656922 + 0.753958i $$0.271858\pi$$
$$744$$ 0 0
$$745$$ 34194.5 1.68160
$$746$$ 0 0
$$747$$ −17395.6 + 23459.0i −0.852035 + 1.14902i
$$748$$ 0 0
$$749$$ 6911.39i 0.337165i
$$750$$ 0 0
$$751$$ 20486.9i 0.995445i 0.867336 + 0.497723i $$0.165830\pi$$
−0.867336 + 0.497723i $$0.834170\pi$$
$$752$$ 0 0
$$753$$ −178.180 353.950i −0.00862318 0.0171297i
$$754$$ 0 0
$$755$$ −6686.04 −0.322291
$$756$$ 0 0
$$757$$ 7557.64 0.362863 0.181431 0.983404i $$-0.441927\pi$$
0.181431 + 0.983404i $$0.441927\pi$$
$$758$$ 0 0
$$759$$ −8282.16 16452.2i −0.396078 0.786797i
$$760$$ 0 0
$$761$$ 7134.66i 0.339857i 0.985456 + 0.169928i $$0.0543537\pi$$
−0.985456 + 0.169928i $$0.945646\pi$$
$$762$$ 0 0
$$763$$ 8802.73i 0.417667i
$$764$$ 0 0
$$765$$ 5548.50 7482.50i 0.262231 0.353634i
$$766$$ 0 0
$$767$$ 6618.03 0.311556
$$768$$ 0 0
$$769$$ −15189.2 −0.712270 −0.356135 0.934434i $$-0.615906\pi$$
−0.356135 + 0.934434i $$0.615906\pi$$
$$770$$ 0 0
$$771$$ 24196.7 12180.8i 1.13025 0.568976i
$$772$$ 0 0
$$773$$ 30376.4i 1.41340i 0.707511 + 0.706702i $$0.249818\pi$$
−0.707511 + 0.706702i $$0.750182\pi$$
$$774$$ 0 0
$$775$$ 6057.64i 0.280770i
$$776$$ 0 0
$$777$$ 9852.69 4959.91i 0.454908 0.229003i
$$778$$ 0 0
$$779$$ −29008.9 −1.33421
$$780$$ 0 0
$$781$$ 863.961 0.0395838
$$782$$ 0 0
$$783$$ 5816.37 33543.7i 0.265466 1.53097i
$$784$$ 0 0
$$785$$ 12661.4i 0.575673i
$$786$$ 0 0
$$787$$ 19109.2i 0.865528i 0.901507 + 0.432764i $$0.142462\pi$$
−0.901507 + 0.432764i $$0.857538\pi$$
$$788$$ 0 0
$$789$$ 15566.7 + 30922.7i 0.702393 + 1.39528i
$$790$$ 0 0
$$791$$ 3143.18 0.141288
$$792$$ 0 0
$$793$$ −1557.27 −0.0697356
$$794$$ 0 0
$$795$$ −11739.5 23320.1i −0.523718 1.04035i
$$796$$ 0 0
$$797$$ 15055.1i 0.669109i −0.942376 0.334554i $$-0.891414\pi$$
0.942376 0.334554i $$-0.108586\pi$$
$$798$$ 0 0
$$799$$ 9041.36i 0.400326i